When θ \theta\,θ is small, show that cosθ2sinθ\displaystyle \frac{\cos \theta}{2\sin \theta}2sinθcosθ can be approximated by 2−θ24θ\displaystyle \frac{2 - \theta^2}{4\theta}4θ2−θ2
Hence, approximate the value of cosπ302sinπ30\displaystyle \frac{\cos \frac{\pi}{30}}{2\sin \frac{\pi}{30}}2sin30πcos30π
Calculate the percentage error in your approximation
317 exam-style questions on OCR A Level Maths 1.5 Trigonometry, covering 1.5.1 Definitions for all arguments, 1.5.2 Sine and cosine rules, 1.5.3 Area of a triangle, 1.5.4 Radian measure (A-level only), 1.5.5 Small angle approximations (A-level only), 1.5.6 Graphs of basic trigonometric functions, 1.5.7 Exact values in radians (A-level only), 1.5.8 Reciprocal and inverse trigonometric ratios (A-level only), 1.5.9 Graphs of reciprocal and inverse functions (A-level only), 1.5.10 Trigonometric identities, 1.5.11 Further trigonometric identities (A-level only), 1.5.12 Double angle and compound angle formulae (A-level only), 1.5.13 Geometrical proofs of formulae (A-level only), 1.5.14 Harmonic form Rcos / Rsin (A-level only), 1.5.15 Trigonometric equations, 1.5.16 Proof involving trigonometric functions (A-level only), and 1.5.17 Trigonometric functions in context. Each one has a worked solution and a mark scheme showing where the marks go.